Which of the following numbers is a factor of 56? ${3,5,9,12,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $56$ by each of our answer choices. $56 \div 3 = 18\text{ R }2$ $56 \div 5 = 11\text{ R }1$ $56 \div 9 = 6\text{ R }2$ $56 \div 12 = 4\text{ R }8$ $56 \div 14 = 4$ The only answer choice that divides into $56$ with no remainder is $14$ $ 4$ $14$ $56$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $56$ $56 = 2\times2\times2\times7 14 = 2\times7$ Therefore the only factor of $56$ out of our choices is $14$. We can say that $56$ is divisible by $14$.